General quantitative genetic properties are derived for the F2 originating from self-fertilisation of hybrid (F1) individuals. These results extend and generalize previous restricted knowledge about this F2. New equations are found for all genotype frequencies, allele frequencies, inbreeding coefficient, genic (additive-genetic) and dominance variances, broadsense and narrowsense heritabilities, and selection potential. The bulk mean is generally lower, and the genotypic variance is generally higher, than those of the F1 and the allogamous F2. Genic and dominance variances for the selfed F2 are very different to the classical counterparts. Their relationships with inbreeding have been investigated, and they are more elaborate than previously considered. The level of inbreeding is constant irrespective of parental combinations, which is different to the inbreeding of an allogamous F2. Selection potential is generally high, and selection advance generally exceeds bulk inbreeding depression. If selection is assisted by dispersion, the autogamous F2 may obtain greater genetic advance than its allogamous counterpart for the same selection pressure. Under conditions of spatially separated F2, swarms, natural selection may be enhanced by selfing.